5: Decide whether the series converges. If so, find its sum. \sum_{n=1}^{\infty} \frac{3}{n(n+1)} \sum_{n=2}^{\infty} \frac{3^{n}-1}{5^{n-2}} Use the Ratio or Root test, to determine whether the series converges or diverges. \sum_{n=1}^{\infty}

\frac{(\ln n)^{2 n}}{n^{n+1}}